An election is held using the method of pairwise comparisons. Suppose that X is

Question

An election is held using the method of pairwise comparisons. Suppose that X is the winner of the election under the method of pairwise comparisons, but due to an election irregularity, there is a irregularity, In the reelection, the only changes are changes that favor X and only X (specifically, you can interpret this to mean that the only changes involve voters who move X up in their ballot without altering the relative order of any of the other candidates). Explain why candidate X must be the winner of the reelection (i.e., the method of pairwise comparisons satisfies the monotonicity criterion).

Explanation / Answer

In the reelection, all the votes that x had got in the first election will b retained by X, because no other candidate can go above X according to the given condition. Also, X have the probability to win some votes from the voters who move X up from 2nd position to first position. So, X will get more votes than what he/she had got in the first election. So, the winner of reelection will be X.

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